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Mixed Strategy in the Superbowl

Game Theory Says Pete Carroll’s Goal-­Line Attempt was Defensible:

http://www.nytimes.com/2015/02/03/upshot/game­theory­says­pete­carrolls­call­at­goal­line­is­d efensible.html?_r=0.​

It was one of the biggest and most questions moments in recent years in sports. The Seattle Seahawks were in the midst of an unlikely comeback and were now a yard away from the endzone. All they needed to do was cross over to the other side to complete the comeback and immortalize themselves as superbowl champions. The Seahawks would fall short, however, making a seemingly inexplicable decisions to pass the ball throw the air, rather than handing the ball to their star running back, aptly nicknamed “Beast Mode” for his ability to break tackles and gain extra yards. The pass was intercepted and the Patriots won the Superbowl due to a horrible decision by the opposing team’s head coach.

According to game theory, however, coach Carroll made the correct choice to throw the ball. Carroll followed the game theory concept of mixed strategy, which is different from a strict best response strategy that many of Carroll’s detractors are supporting by laying blame upon him. In a best response strategy, a player’s best strategy is the same regardless of what his opponent is doing. This is what the Prisoner’s Dilemma presents its players, as their best response is always to confess in order to gain fewer years in prison. In the Superbowl, however, Carroll had a mixed strategy, where he had two options: run or pass. His opponent had two options: defend the run or defend the pass. A mixed strategy dictates that in order to maximize success rate, one must choose each option with a certain probability. If Carroll’s team always ran the ball, there would be zero probability that they are passing, violating the mixed strategy principle. On the field, this would allow the Patriots to o​nly​defend against the run, severely limiting the probability for the success of the play.

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